x^2-56x+96=0

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Solution for x^2-56x+96=0 equation: 


Simplifying
x2 + -56x + 96 = 0

Reorder the terms:
96 + -56x + x2 = 0

Solving
96 + -56x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-96' to each side of the equation.
96 + -56x + -96 + x2 = 0 + -96

Reorder the terms:
96 + -96 + -56x + x2 = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -56x + x2 = 0 + -96
-56x + x2 = 0 + -96

Combine like terms: 0 + -96 = -96
-56x + x2 = -96

The x term is -56x.  Take half its coefficient (-28).
Square it (784) and add it to both sides.

Add '784' to each side of the equation.
-56x + 784 + x2 = -96 + 784

Reorder the terms:
784 + -56x + x2 = -96 + 784

Combine like terms: -96 + 784 = 688
784 + -56x + x2 = 688

Factor a perfect square on the left side:
(x + -28)(x + -28) = 688

Calculate the square root of the right side: 26.229754097

Break this problem into two subproblems by setting 
(x + -28) equal to 26.229754097 and -26.229754097.


Subproblem 1
x + -28 = 26.229754097

Simplifying
x + -28 = 26.229754097

Reorder the terms:
-28 + x = 26.229754097

Solving
-28 + x = 26.229754097

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '28' to each side of the equation.
-28 + 28 + x = 26.229754097 + 28

Combine like terms: -28 + 28 = 0
0 + x = 26.229754097 + 28
x = 26.229754097 + 28

Combine like terms: 26.229754097 + 28 = 54.229754097
x = 54.229754097

Simplifying
x = 54.229754097


Subproblem 2
x + -28 = -26.229754097

Simplifying
x + -28 = -26.229754097

Reorder the terms:
-28 + x = -26.229754097

Solving
-28 + x = -26.229754097

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '28' to each side of the equation.
-28 + 28 + x = -26.229754097 + 28

Combine like terms: -28 + 28 = 0
0 + x = -26.229754097 + 28
x = -26.229754097 + 28

Combine like terms: -26.229754097 + 28 = 1.770245903
x = 1.770245903

Simplifying
x = 1.770245903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.229754097, 1.770245903}

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